Simplify the following expression: $ q = \dfrac{10k + 5}{-8k - 7} - \dfrac{-9}{4} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{10k + 5}{-8k - 7} \times \dfrac{4}{4} = \dfrac{40k + 20}{-32k - 28} $ Multiply the second expression by $\dfrac{-8k - 7}{-8k - 7}$ $ \dfrac{-9}{4} \times \dfrac{-8k - 7}{-8k - 7} = \dfrac{72k + 63}{-32k - 28} $ Therefore $ q = \dfrac{40k + 20}{-32k - 28} - \dfrac{72k + 63}{-32k - 28} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{40k + 20 - (72k + 63) }{-32k - 28} $ Distribute the negative sign: $q = \dfrac{40k + 20 - 72k - 63}{-32k - 28}$ $q = \dfrac{-32k - 43}{-32k - 28}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{32k + 43}{32k + 28}$